Kane’s Equations for Haptic Display of Multibody Systems
R. Brent Gillespie
Haptics-e, The Electronic Journal for Haptics Research, Vol 2., No. 3., 18
August 2003, http://www.haptics-e.org
The design of a general-purpose multibody simulator that runs in real-time and
features haptic display is presented. The repertoire of this simulator includes
systems subject to holonomic constraints, nonholonomic constraints, and notably,
systems subject to changing constraints. In contrast to the use of generic
equations of motion, Kane’s method is used by a computerized symbolic
manipulator to produce custom-built, compact, and computationally efficient
ordinary differential equations for each virtual system to be simulated. A
method is presented whereby new equations, reflecting the presence of a
transient constraint, may be formulated on-line by a recombination of terms
comprising the nominal equations. This paper also serves as a tutorial
introduction to Kane’s method and includes a detailed derivation of Kane’s
equations with a geometric interpretation. An illustrative example
featuring changing constraint conditions is developed in the body of the paper
while two more examples, chosen to highlight certain features within Kane’s
method, are presented at the conclusion.